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DAT Quantitative Reasoning with 100% correct answers
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DAT Quantitative ReasoningDistance -✅✅-d= rate(time)
Average Rate - ✅✅-total distance/total time
Slope Formulas - ✅✅-y=mx+b
m- slope
b- y intercept
Given 2 points:
y2-y1=m(x2-x1)
m= (y2-y1)/(x2-x1)
Parallel and Perpendicular Lines - ✅✅-Parallel- Slopes must be equal
Perpendicular- Slopes will be negative reciprocal: -(flipped)
Distance Between Two Points - ✅✅-Make a right triangle and solve for the
hypotenuse with a^2+b^2=c^2. Or:
d= √(x2-x1)^2+(y2-y1)^2
Midpoint - ✅✅-Average together the x values and y values. Or:
[(x1+x2/2), (y1+y2/2)]
Important Conversions - ✅✅-K= C + 273
F= 9/5(C)+32
0C=32F
1 in = 2.54 cm
1 mi = 5280 ft
1 ft = 12 in
1 yd = 3 ft
1 m = 1.1 yd
1 kg = 2.2 lbs
1 lb = 454 g = 16 oz
Quadratic Equations - ✅✅-For any equation in the format: ax^2 + bx + c = 0
(x+y)(x-y) = x²-y²
, (x+y)² = x² + 2xy + y²
(x-y)² = x² - 2xy - y²
Multiplying Exponents (with the same base) - ✅✅-(x^a)(x^b)= x^a+b
Add the exponents.
Dividing Exponents (with the same base) - ✅✅-x^a/x^b = x^a-b
Subtract the exponents.
Exponent to the power of another number - ✅✅-(x^a)^b = x^a*b
Multiply the exponents.
Multiplying Exponents (with different bases) - ✅✅-(x^b)(y^b)=(xy)^b
Multiply those two bases and have them to the og exponent.
Dividing Exponents (with different bases) - ✅✅-(x^b/y^b) = (x/y)^b
Divide those two bases and have them to the og exponent.
Exponent Rules Overview - ✅✅-a^n ⋅ a^m = a^n+m
a^n ⋅ b^n = (a ⋅ b)^n
a^n / a^m = a^n-m
a^n / b^n = (a / b)^n
(a^n)^m = a nxm
1/X^n = - ✅✅-x^-n
Adding Logs - ✅✅-log(x) + log(y) = log(x*y)
Subtracting Logs - ✅✅-log(x) - log(y) = log(x/y)
log(base a)x^b - ✅✅-b*log(base a)x
Bring the exponent to the front and multiply.
How to solve log x = b - ✅✅-x= 10^b
Percent Change - ✅✅-(x2-x1)/x1 *100
u- ✅✅-Union. Includes all data excluding duplicate values.
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